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## A tough limit

Multivariate Calculus
Grigorios Kostakos
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### A tough limit

Examine if the limit $$\displaystyle\mathop{\lim}\limits_{(x,y)\to(1,1)}{\frac{x^y-y\,(x-1)-1}{x^2+y^2-2\,(x+y-1)}}$$ exists and if does exists, calculate it.

NOTE: I've got an (almost) solution.
Grigorios Kostakos
Grigorios Kostakos
Founder
Articles: 0
Posts: 460
Joined: Mon Nov 09, 2015 1:36 am
Location: Ioannina, Greece

### Re: A tough limit

The function $f(x,y)=x^y\,,\; (x,y)\in{\mathbb{R}}^2\,,$ is at least twice continuously differentiable in a open disk with centre $(1,1)$ and its 2nd degree Taylor polynomial is
\begin{align*}